Given that the sum of the polynomial 2x & # 710; 2 + my-12 and the polynomial NX & # 710; 2-3y + 6 does not contain x, y, try to find the value of Mn It is known that 3A & # 710; x1b and ab are similar terms, 3A & # 710; x2b and a & # 710; 2B are similar terms, 3A & # 710; x3b and a & # 710; 3b are similar terms,..., 3A & # 710; XKB and AKB are similar terms, find 1 / x1x2 + 1 / x2x3 + 1 / x3x4 +... + 1 / x49x50

Given that the sum of the polynomial 2x & # 710; 2 + my-12 and the polynomial NX & # 710; 2-3y + 6 does not contain x, y, try to find the value of Mn It is known that 3A & # 710; x1b and ab are similar terms, 3A & # 710; x2b and a & # 710; 2B are similar terms, 3A & # 710; x3b and a & # 710; 3b are similar terms,..., 3A & # 710; XKB and AKB are similar terms, find 1 / x1x2 + 1 / x2x3 + 1 / x3x4 +... + 1 / x49x50

The sum of 2x & # 710; 2 + my-12 and polynomial NX & # 710; 2-3y + 6 does not contain x, y
2xˆ2+my-12+nxˆ2-3y+6
=(n+2)x^2+(m-3)y-6
∴m=3
∴mn=3n
If the title is changed to 2x & # 710; 2 + my-12 and the sum of polynomial NX & # 710; 2-3y + 6 does not contain x ^ 2, Y:
2xˆ2+my-12+nxˆ2-3y+6
=(n+2)x^2+(m-3)y-6
∴m=3,n=-2
∴mn=3*(-2)=-6
[supplementary questions]
3A & # 710; x1b and ab are of the same kind, X1 = 1
3A & # 710; x2b and a & # 710; 2B are of the same kind, X2 = 2
3A & # 710; x3b and a & # 710; 3b are of the same kind, X3 = 3
...,
3A & # 710; XKB and AKB are the same kind, XK = K
1/x1x2+1/x2x3+1/x3x4+...+1/x49x50
=1/(1*2)+1/(2*3)+1/(3*4)+...+(1/(49*50)
=1/1-1/2+1/2-1/3+.-1/49+1/49-1/50
=1-1/50
=49/50

Factorization of x ^ 2-4xy + 3Y ^ 2

Original formula = (x-3y) * (X-Y)

The following factorization: ① x3-4x = x (x2-4); ② a2-3a + 2 = (A-2) (A-1); ③ a2-2a-2 = a (A-2) - 2; ④ x2 + X + 14 = (x + 12) 2______ (fill in the serial number only)

① If the decomposition is not complete, it should be x3-4x = x (x + 2) (X-2), so this option is wrong; ② a2-3a + 2 = (A-2) (A-1), correct; ③ a2-2a-2 = a (A-2) - 2, the right side is not in the form of product, so this option is wrong; ④ x2 + X + 14 = (x + 12) 2, correct

The following factorizations are correct: 1. X ^ 3-4x = x (x ^ 2-4) 2. A ^ 2-3a + 2 = (A-2) (A-1) 3. A ^ 2-2a-2 = a (A-2) - 2
4.x^2+x+1/4=(x+1/2)

The first three are correct, the fourth should be (x + 1 / 2) ^ 2

Given that x = half of the equation, two fourths of x-m-one-half = one-third of x minus m root, find the algebraic formula
The value of quarter (- 4m square + 2m-8) - (half m minus 1)

The value of quarter (- 4m square + 2m-8) - (half m minus 1)
(-4m^2+2m-8)/4-(m/2-1)=-m^2+m/2-2-m/2+1=-m^2-1
Theory with known conditions
1. "X equals half the root of the equation 2 / 4 * (x-m) - 1 / 2 = x / 3-m"
First, find the root of the equation 2 / 4 * (x-m) - 1 / 2 = x / 3-m. if there is no difference in variables, we can change x into y
Then 2 / 4 * (y-m) - 1 / 2 = Y / 3-m
y/2-m/2=y/3-m
Y / 6 = - M / 2
So y = - 3M
Then x = Y / 2 = - 3m / 2
This is obviously unable to find the value of the following algebraic expression, so it is discarded
2. "X = 1 / 2 is the root of the equation 2 / 4 * (x-m) - 1 / 2 = x / 3-m"
In this case, the root of the equation 2 / 4 * (x-m) - 1 / 2 = x / 3-m is x = - 3M = 1 / 2
Then M = - 1 / 6
The value of the algebraic formula is (- 4m ^ 2 + 2m-8) / 4 - (M / 2-1) = - m ^ 2-1 = - (- 1 / 6) ^ 2-1 = - 37 / 36

When k is the value, the inequality 1 / 2 (KX + 8) > 3 holds
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Simplify
1 / 2 k x + 1 > 0
We can see that k = 0 holds

Solve the inequality (3x + 2) / 4 - (x-1) / 2 ＞ 0 and find its non positive integer solution
Solve the inequality (3x + 2) / 4 - (x-1) / 2 ＞ 0 and find its non positive integer solution

That is: (3x + 2) / 4-2 (x-1) / 4 > 0 (3x-2x + 2 + 2) / 4 > 0 (x + 4) / 4 > 0, so the solution of x > - 4 is: - 3, - 2, - 1,0

The number of positive integer solutions of inequality 2x-1 ≥ 3x-5 is ()
A. 1B. 2C. 3D. 4

Transfer the term to get: 2x-3x ≥ - 5 + 1, merge the similar term to get: - x ≥ - 4, change the coefficient to 1, get: X ≤ 4 inequality 2x-1 ≥ 3x-5, the positive integer solution is 1, 2, 3, 4. So choose D

Known inequality x square - 3x + T

I didn't understand what you wrote

Solving inequality LG (x ^ 2-3x-4) - LG (x + 5) ≥ LG2

lg(x^2-3x-4)-lg(x+5)≥lg2
so lg(x^2-3x-4)≥lg(x+5)+lg2=lg2(x+5)
so x^2-3x-4>=2(x+5)
so x^2-5x-14>=0
so (x+2)(x-7)>=0
so x>=7 or x0
x+5>0
Solve them all, and then take the intersection